Continuous function

Related lectures (30)

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Revisits the definitions of continuous functions, emphasizing isolated points and limits.

Explores the extension of functions and the conditions for continuity.

Explores the necessity of uniform continuity for continuous functions on compact sets.

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Explores abstract integration of functions and the need for stronger conditions beyond continuity.

Explores the Stone-Weierstrass theorem, proving uniform density of specific function families on compact sets.

Covers the bisection method proposition and its demonstration for finding roots.

Explains vector functions and the parameterization of curves with examples.

Covers the properties of continuous functions and explores inverse and injective functions with examples.

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